Trajectory planning and control of an underactuated planar 2R manipulator

The problem of regulation of an underactuated planar 2R manipulator is solved by tracking appropriated off-line planned trajectories. A class of parametric trajectories is proposed to reach a desired configuration. An optimization algorithm is proposed to find the parameters. Besides, a feedback control is proposed to regulate the manipulator under error modeling and small deviations on the initial conditions. By using simulations, it is illustrated that if the coordinates of the underactuated system track the planned trajectories then the system reaches the desired configuration.

[1]  Yangsheng Xu,et al.  Planning collision-free motions for underactuated manipulators in constrained configuration space , 1997, Proceedings of International Conference on Robotics and Automation.

[2]  Naoji Shiroma,et al.  Nonholonomic control of a three-DOF planar underactuated manipulator , 1998, IEEE Trans. Robotics Autom..

[3]  Joseph L. Jones,et al.  Mobile robots , 1993 .

[4]  Mrdjan Jankovic,et al.  TORA example: cascade- and passivity-based control designs , 1996, IEEE Trans. Control. Syst. Technol..

[5]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[6]  Isabelle Fantoni,et al.  Passivity Based Control of the Inverted Pendulum , 1998 .

[7]  Mark W. Spong,et al.  Energy Based Control of a Class of Underactuated Mechanical Systems , 1996 .

[8]  Anthony A. Maciejewski,et al.  Fault tolerance for kinematically redundant manipulators: anticipating free-swinging joint failures , 1998, IEEE Trans. Robotics Autom..

[9]  Naomi Ehrich Leonard,et al.  Stabilization of mechanical systems using controlled Lagrangians , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  R. Mattone,et al.  Control of underactuated mechanical systems: application to the planar 2R robot , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  Giuseppe Oriolo,et al.  Free-joint manipulators: motion control under second-order nonholonomic constraints , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[12]  Naoji Shiroma,et al.  Time-scaling control of an underactuated manipulator , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[13]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[14]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[15]  Mark W. Spong,et al.  Underactuated mechanical systems , 1998 .

[16]  Woojin Chung,et al.  Design of a nonholonomic manipulator , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[17]  J. W. Humberston.  Classical mechanics , 1980, Nature.